SOUTH COUNTY  A U.S. Border Patrol agent fatally shot a man who officials said assaulted him with a barrage of rocks in rugged terrain near the Otay Mesa border crossing Tuesday morning, reigniting a debate over whether agents should use lethal force against rock throwers.

The shooting occurred about 6:40 a.m. in a mountainous area some four miles east of the border crossing, sheriff’s homicide Lt. Glenn Giannantonio said.

Two agents were tracking two men suspected of entering the United States illegally when one of the agents moved to a location to cut off the fleeing border-crossers, Giannantonio said.

The agents were about a quarter mile apart and out of each other’s sight when one of them came across a third man and told him in English and Spanish to stop, but he ran away, the lieutenant said.

The agent chased after the man, following him into a ravine, Giannantonio said. The man then ran up the opposite hillside and was above the agent.

He pelted the agent with fist-sized rocks, despite repeated requests to stop, Giannantonio said. The agent deflected some of the rocks with his hands, even as the size of them got larger. One was about the size of a basketball, the lieutenant said.

A larger rock hit the agent in the head.

“Fearing that another rock strike to the head could kill or incapacitate him, the agent fired his duty pistol at least twice at the man, striking him,” Giannantonio said.

The agent tried to revive the man, but he died at the scene.

The two men originally being tracked were taken into custody and are expected to face charges for entering the United States illegally.

The agent, whose name was not released, suffered minor injuries, and was treated and released from a hospital. He has been placed on paid administrative leave, as is routine in such shootings.

Assistant Chief Patrol Agent Rosario Vasquez said the location where the shooting occurred is called the “white cross” area, and is regularly patrolled. Drug- and human-trafficking activity frequently occurs there.

“The agents are out there every day trying to protect our borders,” said Vasquez. “It’s unfortunate that a situation like this had to happen. It’s the last thing we want to see.”

Since 2010, Customs and Border Protection agents and officers have been involved in more than 20 fatal incidents, including five in San Diego. Nine involved rock throwing, including Tuesday’s.

In November, Border Patrol Chief Mike Fisher said that the agency would not change its use-of-force policy, which allows lethal weapons to be used against rock throwers. Fisher said that making exceptions in certain situations “was very problematic and could potentially put Border Patrol agents in danger.”

His comments came in response to a recommendation by the Police Executive Research Forum, a nonprofit police research and policy organization, that agents should stop using lethal force against rock throwers.

The shooting Tuesday was the first involving rock throwers since the research forum audited the Border Patrol at its request.

The group’s report also said agents along the Southwest border were assaulted 6,095 times between 2006 and 2012.

Shawn Moran, vice president of the national union for Border Patrol agents, supports agents being allowed to shoot rock throwers.

“The solution to these incidents is if you don’t want to get shot, don’t assault a Border Patrol agent,” said Moran, who is based in San Diego.

Agents carry at least one non-lethal weapon, he said, but they will decide how to respond in the moment, which may mean firing their gun.

“When the agent only suffers a minor injury, people may say it’s a disproportionate use of force,” Moran said. “It’s easy to second guess the choice after the fact, but these things happen in split seconds. It’s not part of the job to get injured.”

Pedro Rios, director of the American Friends Service Committee in San Diego, which works on behalf of immigrants, said Tuesday’s shooting points to the need for President Barack Obama to rein in an out-of-control agency.

“Until then, we will continue to see these type of cases that will be investigated in a non-transparent way, there won’t be proper resolution and they’ll be repeated over and over,” Rios said.

Sixteen members of Congress in 2012 requested the U.S. Department of Homeland Security review use-of-force incidents and practices by Customs and Border Protection after PBS aired a documentary that showed a 42-year-old man being fatally beaten and shot with a Taser while surrounded by more than a dozen border officers and agents at the San Ysidro crossing.

The inspector general’s report, issued last year, found that the agency doesn’t track all use-of-force allegations and that “many agents and officers” surveyed in an internal 2012 audit didn’t understand when they could or couldn’t use force.

The beating of Anastasio Hernandez Rojas, who lived in Santee, was captured on cellphone video by a bystander. It showed him hogtied and crying for help as he was kicked, hit with batons and shot with a Taser. His family has filed a wrongful death lawsuit.

Officials have said Hernandez Rojas was resisting attempts to return him to Mexico when he died at the hands of federal law enforcement officers in May 2010.